Homotopy type and $A_\infty$-group structure

The aim of the paper is to define and study algebraic operations closely related to the group structure on the homotopy groups of topological spaces. These are certain many-place operations on the homotopy groups. The family of these operations induces an algebraic structure on the homotopy groups, which is called an $A_\infty$-group structure by analogy with the $A_\infty$-structures introduced by Stasheff.